✦ LIBER ✦

The chromaticity of wheels with a missing spoke II

✍ Scribed by G.L. Chia

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 309 KB
Volume: 148
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00248-h

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✦ Synopsis

In the previous paper, it was shown that the graph U. ÷ 1 obtained from the wheel W n ÷ 1 by deleting a spoke is uniquely determined by its chromatic polynomial if n >i 3 is odd. In this paper, we show that the result is also true for even n >~ 4 except when n = 6 in which case, the graph W given in the paper is the only graph having the same chromatic polynomial as that of U 7. The relevant tool is the notion of nearly uniquely colorable graph.

As in [2], only finite undirected graphs without loops or multiple edges will be considered. A graph G is chromatically unique if it is uniquely determined by its chromatic polynomial P(G;2). The wheel IV.+ 1 is obtained by taking the join of a single vertex and the cycle Cn on n vertices. The graph U.+ ~ is obtained from Wn÷l by deleting a spoke which is an edge joining the single vertex to a vertex on Cn.

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